Blender Game engine Animation Not playing
I can't open your file from here. 

You need at least the armature modifier. You can easily get them by


select the skin mesh object(s)
shift select the armature
ctrl+p Set Parent To \ Armature Deform


Usually you need Vertex Groups set that match the names of the armature's bones. 

ctrl+p Set Parent To \ Armature Deform \ With ... allows you to create such Vertex Groups.

I hope it helps